Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative

Zhijie Xiao

Journal of Time Series Analysis, 2001, vol. 22, issue 1, 87-105

Abstract: We propose a new test for the null hypothesis that a time series is stationary around a deterministic trend. The test is valid under general conditions on stationarity. Asymptotic distributions of the test statistic are derived under both the null and the alternative hypothesis of a unit root. It is shown that the limiting distribution has the classical Kolmogoroff– Smirnoff form. Critical values for the null distribution are calculated. Consistency of the tests is proved. The tests provide a useful complement to the conventional unit root tests.

Date: 2001
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